University Calculus Tutors

Calculus I (MATH 101)

This course introduces the fundamental concepts of calculus, including limits, derivatives, and the basics of integration, with a focus on applications in various fields.

Calculus II (MATH 102)

Building on Calculus I, this course covers advanced techniques of integration, sequences and series, and introduces differential equations, emphasizing their applications.

Multivariable Calculus (MATH 201)

This course expands calculus to functions of several variables, covering topics such as partial derivatives, multiple integrals, and vector calculus, with applications to physical sciences.

Differential Equations (MATH 202)

An introduction to ordinary differential equations, this course explores methods for solving various types of equations and their applications in modeling real-world phenomena.

Calculus for Business and Social Sciences (MATH 103)

Designed for students in business and social sciences, this course emphasizes the application of calculus concepts to business models, optimization, and economic theories.

Calculus with Analytic Geometry (MATH 104)

This course integrates calculus and analytic geometry, focusing on functions, limits, derivatives, and integrals, while incorporating geometric interpretations.

Engineering Calculus (MATH 105)

Tailored for engineering students, this course covers single-variable calculus with an emphasis on problem-solving techniques and applications relevant to engineering disciplines.

Calculus III (MATH 201)

This course extends the concepts of calculus to three-dimensional space, covering topics such as vector functions, partial derivatives, multiple integrals, and line and surface integrals.

Differential Equations II (MATH 202)

Building on the foundations of differential equations, this course focuses on advanced techniques for solving linear and nonlinear differential equations and their applications in various fields.

Advanced Calculus (MATH 203)

This course provides a rigorous treatment of calculus topics, including sequences and series of functions, uniform convergence, and the theory of integration, emphasizing proof and theoretical understanding.

Numerical Methods (MATH 204)

This course introduces numerical techniques for solving mathematical problems, including root-finding algorithms, numerical integration, and differential equations, with applications in engineering and the sciences.

Real Analysis (MATH 205)

Focusing on the theoretical aspects of calculus, this course covers limits, continuity, differentiability, and integrability, with an emphasis on formal proofs and the foundations of analysis.

Complex Variables (MATH 206)

This course explores functions of complex variables, covering topics such as analytic functions, contour integration, and the residue theorem, with applications in physics and engineering.

Mathematical Modeling (MATH 207)

This course emphasizes the development and analysis of mathematical models to solve real-world problems, integrating techniques from calculus, differential equations, and numerical methods.

Limits and Continuity

• Understanding the concept of limits and how they apply to functions.
• Evaluating limits using various techniques, including direct substitution and factoring.
• Exploring the concept of continuity and identifying points of discontinuity.

Derivatives

• Learning the definition of the derivative and its geometric interpretation as the slope of a tangent line.
• Applying differentiation rules, including the product, quotient, and chain rules.
• Exploring applications of derivatives, such as finding critical points, determining concavity, and solving optimization problems.

Integrals

• Understanding the concept of the definite and indefinite integral.
• Learning various techniques of integration, including substitution and integration by parts.
• Applying integrals to calculate areas under curves and solving problems in physics and engineering.

Multivariable Calculus

• Extending calculus concepts to functions of several variables.
• Exploring partial derivatives and their applications.
• Learning about multiple integrals and vector calculus, including line and surface integrals.

Differential Equations

• Introducing ordinary differential equations and their applications.
• Learning methods for solving first-order and second-order differential equations.
• Applying differential equations to model real-world phenomena in science and engineering.

Series and Sequences

• Understanding sequences and the concept of convergence.
• Exploring infinite series and tests for convergence.
• Learning about power series and Taylor series expansions.

Applications of Calculus

• Applying calculus concepts to real-world problems, including rates of change and motion.
• Exploring the use of calculus in fields such as physics, biology, and economics.
• Understanding the role of calculus in modeling and analyzing complex systems.